On the Uniqueness of Image Flow Solutions for Planar Surfaces in Motion
MARYLAND UNIV COLLEGE PARK CENTER FOR AUTOMATION RESEARCH
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Two important results relating to the uniqueness of image flow solutions for planar surfaces in motion are presented here. These results relate to the formulation of the image flow problem by Waxman and Ullman which is based on a kinematic analysis of the image flow field. The first result concerns resolving the duality of interpretations that are generally associated with the instantaneous image flow of an evolving image sequence. It is shown that the interpretation for orientation and motion of planar surfaces is unique when either two successive image flows of one planar surface patch are given or one image flow of two planar patches moving as a rigid body is given. This document has proved this by driving explicit expressions for the evolving solution of an image flow sequence with time. These expressions can be used to resolve this ambiguity of interpretation in practical problems. The second result is the proof of uniqueness for the velocity of approach which satisfies the image flow equations for planar surfaces derived in Waxmans and Ullmans document. In addition, it is shown that this velocity can be computed as the middle root of a cubic equation. These two results together suggest a new method for solving the image flow problem for planar surfaces in motion. Additional keywords image flow equations.
- Numerical Mathematics
- Fluid Mechanics